The cyclic subgroup of Z_24 generated by 18 has order,4,8,12,6,A
Find the order of the factor group Z_6/<3>.,2,3,6,12,B
Statement 1 | A permutation that is a product of m even permutations and n odd permutations is an even permutation if and only if n is even. Statement 2 | Every group is isomorphic to a group of permutations.,"True, True","False, False","True, False","False, True",A
Find the order of the factor group (Z_4 x Z_12)/(<2> x <2>),2,3,4,12,C
Find the maximum possible order for some element of Z_4 x Z_6.,4,6,12,24,C
Statement 1 | The symmetric group S_3 is cyclic. Statement 2 | Every group is isomorphic to some group of permutations.,"True, True","False, False","True, False","False, True",D
"Statement 1 | If a and b are elements of finite order in an Abelian group, then |ab| is the lcm (|a|,|b|). Statement 2 | If g is a group element and g^n = e, then |g| = n.","True, True","False, False","True, False","False, True",B
"Statement 1 | If f is a homomorphism from G to K and H is normal in G then f(H) is normal in K. Statement 2 | If f is a homomorphism from G to a group and H is finite subgroup of G, then |f(H)| divides |H|.","True, True","False, False","True, False","False, True",D
Find the maximum possible order for an element of S_n for n = 7.,6,12,30,105,B
Statement 1 | Every integral domain has a field of quotients. Statement 2 | A polynomial of degree n over a ring can have at most n zeros counting multiplicity.,"True, True","False, False","True, False","False, True",C
"Statement 1 | If a group has an element of order 10, then the number of elements of order 10 is divisible by 4. Statement 2 | If m and n are positive integers and phi is the Euler phi function, then phi(mn) = phi(m)phi(n).","True, True","False, False","True, False","False, True",B
